Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.bulsci.2015.06.002 http://hdl.handle.net/11449/171894 |
Resumo: | Detect the birth of limit cycles in non-smooth vector fields is a very important matter into the recent theory of dynamical systems and applied sciences. The goal of this paper is to study the bifurcation of limit cycles from a continuum of periodic orbits filling up a two-dimensional isochronous cylinder of a vector field in R3. The approach involves the regularization process of non-smooth vector fields and a method based in the Malkin bifurcation function for C0 perturbations. The results provide sufficient conditions in order to obtain limit cycles emerging from the cylinder through smooth and non-smooth perturbations of it. To the best of our knowledge they also illustrate the implementation by the first time of a new method based in the Malkin bifurcation function. In addition, some points concerning the number of limit cycles bifurcating from non-smooth perturbations compared with smooth ones are studied. In summary the results yield a better knowledge about limit cycles in non-smooth vector fields in R3 and explicit a manner to obtain them by performing non-smooth perturbations in codimension one Euclidean manifolds. |
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Repositório Institucional da UNESP |
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Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinderLimit cyclesMalkin's bifurcation functionNon-smooth vector fieldsDetect the birth of limit cycles in non-smooth vector fields is a very important matter into the recent theory of dynamical systems and applied sciences. The goal of this paper is to study the bifurcation of limit cycles from a continuum of periodic orbits filling up a two-dimensional isochronous cylinder of a vector field in R3. The approach involves the regularization process of non-smooth vector fields and a method based in the Malkin bifurcation function for C0 perturbations. The results provide sufficient conditions in order to obtain limit cycles emerging from the cylinder through smooth and non-smooth perturbations of it. To the best of our knowledge they also illustrate the implementation by the first time of a new method based in the Malkin bifurcation function. In addition, some points concerning the number of limit cycles bifurcating from non-smooth perturbations compared with smooth ones are studied. In summary the results yield a better knowledge about limit cycles in non-smooth vector fields in R3 and explicit a manner to obtain them by performing non-smooth perturbations in codimension one Euclidean manifolds.Department of Mathematics IBILCE-UNESP Univ. Estadual Paulista, Rua Cristovão Colombo 2265, Jardim NazarethDepartment of Physics Chemistry and Mathematics UFSCarDepartment of Mathematics IBILCE-UNESP Univ. Estadual Paulista, Rua Cristovão Colombo 2265, Jardim NazarethUniversidade Estadual Paulista (Unesp)Universidade Federal de São Carlos (UFSCar)Buzzi, C. A. [UNESP]Euzébio, R. D. [UNESP]Mereu, A. C.2018-12-11T16:57:37Z2018-12-11T16:57:37Z2016-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article519-540application/pdfhttp://dx.doi.org/10.1016/j.bulsci.2015.06.002Bulletin des Sciences Mathematiques, v. 140, n. 5, p. 519-540, 2016.0007-4497http://hdl.handle.net/11449/17189410.1016/j.bulsci.2015.06.0022-s2.0-849314322222-s2.0-84931432222.pdf66828677607174450000-0003-2037-8417Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBulletin des Sciences Mathematiques0,960info:eu-repo/semantics/openAccess2024-01-12T06:27:56Zoai:repositorio.unesp.br:11449/171894Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:47:29.627815Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder |
title |
Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder |
spellingShingle |
Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder Buzzi, C. A. [UNESP] Limit cycles Malkin's bifurcation function Non-smooth vector fields |
title_short |
Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder |
title_full |
Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder |
title_fullStr |
Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder |
title_full_unstemmed |
Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder |
title_sort |
Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder |
author |
Buzzi, C. A. [UNESP] |
author_facet |
Buzzi, C. A. [UNESP] Euzébio, R. D. [UNESP] Mereu, A. C. |
author_role |
author |
author2 |
Euzébio, R. D. [UNESP] Mereu, A. C. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Federal de São Carlos (UFSCar) |
dc.contributor.author.fl_str_mv |
Buzzi, C. A. [UNESP] Euzébio, R. D. [UNESP] Mereu, A. C. |
dc.subject.por.fl_str_mv |
Limit cycles Malkin's bifurcation function Non-smooth vector fields |
topic |
Limit cycles Malkin's bifurcation function Non-smooth vector fields |
description |
Detect the birth of limit cycles in non-smooth vector fields is a very important matter into the recent theory of dynamical systems and applied sciences. The goal of this paper is to study the bifurcation of limit cycles from a continuum of periodic orbits filling up a two-dimensional isochronous cylinder of a vector field in R3. The approach involves the regularization process of non-smooth vector fields and a method based in the Malkin bifurcation function for C0 perturbations. The results provide sufficient conditions in order to obtain limit cycles emerging from the cylinder through smooth and non-smooth perturbations of it. To the best of our knowledge they also illustrate the implementation by the first time of a new method based in the Malkin bifurcation function. In addition, some points concerning the number of limit cycles bifurcating from non-smooth perturbations compared with smooth ones are studied. In summary the results yield a better knowledge about limit cycles in non-smooth vector fields in R3 and explicit a manner to obtain them by performing non-smooth perturbations in codimension one Euclidean manifolds. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-06-01 2018-12-11T16:57:37Z 2018-12-11T16:57:37Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.bulsci.2015.06.002 Bulletin des Sciences Mathematiques, v. 140, n. 5, p. 519-540, 2016. 0007-4497 http://hdl.handle.net/11449/171894 10.1016/j.bulsci.2015.06.002 2-s2.0-84931432222 2-s2.0-84931432222.pdf 6682867760717445 0000-0003-2037-8417 |
url |
http://dx.doi.org/10.1016/j.bulsci.2015.06.002 http://hdl.handle.net/11449/171894 |
identifier_str_mv |
Bulletin des Sciences Mathematiques, v. 140, n. 5, p. 519-540, 2016. 0007-4497 10.1016/j.bulsci.2015.06.002 2-s2.0-84931432222 2-s2.0-84931432222.pdf 6682867760717445 0000-0003-2037-8417 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Bulletin des Sciences Mathematiques 0,960 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
519-540 application/pdf |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129461893201920 |